The objective of this research is to obtain satisfactory kinetic models for the understanding of hemoglobin and myoglobin ligand binding. Such a model does not yet exist for any hemoglobin. Studies on a co-operative dimeric hemoglobin by laser-photolysis, modulated photolysis, stopped-flow and temperature jump relaxation should provide enough information for the extraction of all independent rate constants in an allosteric-type model. The dimer is the system of choice because it is the simplest possible co-operative molecule, and, unlike the case for a tetrameric hemoglobin, all rate constants in simple kinetic schemes can be unambiguously determined. In tetrameric and larger hemoglobins, protein dissociation is thermodynamically linked to ligand-binding. We have begun a unique program for measuring directly, by laser- light-scattering stopped-flow the rates for subunit association and hemoglobin dissociation and the equilibrium constants by relaxation. The kinetics monitored by light-scattering differ markedly from those measured by adsorbance changes, showing that dissociation of tetrameric hemoglobin is a very complex process. Combined ligand kinetics and light-scattering studies will provide rate constants for species of defined molecular weight. All instruments are interfaced to a minicomputer with 32K words of memory for data acquisition and reduction. Numerous combined numerical integration and digital minimization computer programs as well as analog computer integration are used for obtaining precise rate constants from the experimental data in terms of theoretical models.